No. Every chart is drawn locally, inside Excel, and nothing sends workbook data anywhere. Like any add-in, each chart loads its code from addins.pythonandvba.com and Microsoft’s office.js. People who only view a workbook make no license call; authors make one license check per author action (opening the editor, Apply, adding a key), which sends the license key, a random installation ID and the add-in version.
Each chart’s settings and a snapshot image of the chart are stored inside your workbook by Office, so they travel with the file. Files you export and share links you copy contain the charted values, because that is their job, but they are created on your machine and go only where you send them. The details are on the privacy page.